Problem: Express your answer as a mixed number simplified to lowest terms. $6\dfrac{6}{14}-1\dfrac{2}{3} = {?}$
Explanation: Simplify each fraction. $= {6\dfrac{3}{7}} - {1\dfrac{2}{3}}$ Find a common denominator for the fractions: $= {6\dfrac{9}{21}}-{1\dfrac{14}{21}}$ Convert ${6\dfrac{9}{21}}$ to ${5 + \dfrac{21}{21} + \dfrac{9}{21}}$ So the problem becomes: ${5\dfrac{30}{21}}-{1\dfrac{14}{21}}$ Separate the whole numbers from the fractional parts: $= {5} + {\dfrac{30}{21}} - {1} - {\dfrac{14}{21}}$ Bring the whole numbers together and the fractions together: $= {5} - {1} + {\dfrac{30}{21}} - {\dfrac{14}{21}}$ Subtract the whole numbers: $=4 + {\dfrac{30}{21}} - {\dfrac{14}{21}}$ Subtract the fractions: $= 4+\dfrac{16}{21}$ Combine the whole and fractional parts into a mixed number: $= 4\dfrac{16}{21}$